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- W2949207034 abstract "The Burrows-Wheeler Transform (BWT) is among the most influential discoveries in text compression and DNA storage. It is a reversible preprocessing step that rearranges an $n$-letter string into runs of identical characters (by exploiting context regularities), resulting in highly compressible strings, and is the basis of the texttt{bzip} compression program. Alas, the decoding process of BWT is inherently sequential and requires $Omega(n)$ time even to retrieve a emph{single} character. We study the succinct data structure problem of locally decoding short substrings of a given text under its emph{compressed} BWT, i.e., with small additive redundancy $r$ over the emph{Move-To-Front} (texttt{bzip}) compression. The celebrated BWT-based FM-index (FOCS '00), as well as other related literature, yield a trade-off of $r=tilde{O}(n/sqrt{t})$ bits, when a single character is to be decoded in $O(t)$ time. We give a near-quadratic improvement $r=tilde{O}(nlg(t)/t)$. As a by-product, we obtain an emph{exponential} (in $t$) improvement on the redundancy of the FM-index for counting pattern-matches on compressed text. In the interesting regime where the text compresses to $n^{1-o(1)}$ bits, these results provide an $exp(t)$ emph{overall} space reduction. For the local decoding problem of BWT, we also prove an $Omega(n/t^2)$ cell-probe lower bound for symmetric data structures. We achieve our main result by designing a compressed partial-sums (Rank) data structure over BWT. The key component is a emph{locally-decodable} Move-to-Front (MTF) code: with only $O(1)$ extra bits per block of length $n^{Omega(1)}$, the decoding time of a single character can be decreased from $Omega(n)$ to $O(lg n)$. This result is of independent interest in algorithmic information theory." @default.
- W2949207034 created "2019-06-27" @default.
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- W2949207034 date "2018-08-12" @default.
- W2949207034 modified "2023-09-23" @default.
- W2949207034 title "Local Decodability of the Burrows-Wheeler Transform" @default.
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